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The recognition of patterns and structures has gained importance for dealing with the growing amount of data being generated by sensors and simulations. Most existing methods for pattern recognition are tailored for scalar data and non-correlated data of higher dimensions. The recognition of general patterns in flow structures is possible, but not yet practically usable, due to the high computation effort. The main goal of this work is to present methods for comparative visualization of flow data, amongst others, based on a new method for efficient pattern recognition on flow data. This work is structured in three parts: At first, a known feature-based approach for pattern recognition on flow data, the Clifford convolution, has been applied to color edge detection, and been extended to non-uniform grids. However, this method is still computationally expensive for a general pattern recognition, since the recognition algorithm has to be applied for numerous different scales and orientations of the query pattern. A more efficient and accurate method for pattern recognition on flow data is presented in the second part. It is based upon a novel mathematical formulation of moment invariants for flow data. The common moment invariants for pattern recognition are not applicable on flow data, since they are only invariant on non-correlated data. Because of the spatial correlation of flow data, the moment invariants had to be redefined with different basis functions to satisfy the demands for an invariant mapping of flow data. The computation of the moment invariants is done by a multi-scale convolution of the complete flow field with the basis functions. This pre-processing computation time almost equals the time for the pattern recognition of one single general pattern with the former algorithms. However, after having computed the moments once, they can be indexed and used as a look-up-table to recognize any desired pattern quickly and interactively. This results in a flexible and easy-to-use tool for the analysis of patterns in 2d flow data. For an improved rendering of the recognized features, an importance driven streamline algorithm has been developed. The density of the streamlines can be adjusted by using importance maps. The result of a pattern recognition can be used as such a map, for example. Finally, new comparative flow visualization approaches utilizing the streamline approach, the flow pattern matching, and the moment invariants are presented.

Modern science utilizes advanced measurement and simulation techniques to analyze phenomena from fields such as medicine, physics, or mechanics. The data produced by application of these techniques takes the form of multi-dimensional functions or fields, which have to be processed in order to provide meaningful parts of the data to domain experts. Definition and implementation of such processing techniques with the goal to produce visual representations of portions of the data are topic of research in scientific visualization or multi-field visualization in the case of multiple fields. In this thesis, we contribute novel feature extraction and visualization techniques that are able to convey data from multiple fields created by scientific simulations or measurements. Furthermore, our scalar-, vector-, and tensor field processing techniques contribute to scattered field processing in general and introduce novel ways of analyzing and processing tensorial quantities such as strain and displacement in flow fields, providing insights into field topology. We introduce novel mesh-free extraction techniques for visualization of complex-valued scalar fields in acoustics that aid in understanding wave topology in low frequency sound simulations. The resulting structures represent regions with locally minimal sound amplitude and convey wave node evolution and sound cancellation in time-varying sound pressure fields, which is considered an important feature in acoustics design. Furthermore, methods for flow field feature extraction are presented that facilitate analysis of velocity and strain field properties by visualizing deformation of infinitesimal Lagrangian particles and macroscopic deformation of surfaces and volumes in flow. The resulting adaptive manifolds are used to perform flow field segmentation which supports multi-field visualization by selective visualization of scalar flow quantities. The effects of continuum displacement in scattered moment tensor fields can be studied by a novel method for multi-field visualization presented in this thesis. The visualization method demonstrates the benefit of clustering and separate views for the visualization of multiple fields.

Due to remarkable technological advances in the last three decades the capacity of computer systems has improved tremendously. Considering Moore's law, the number of transistors on integrated circuits has doubled approximately every two years and the trend is continuing. Likewise, developments in storage density, network bandwidth, and compute capacity show similar patterns. As a consequence, the amount of data that can be processed by today's systems has increased by orders of magnitude. At the same time, however, the resolution of screens has hardly increased by a factor of ten. Thus, there is a gap between the amount of data that can be processed and the amount of data that can be visualized. Large high-resolution displays offer a way to deal with this gap and provide a significantly increased screen area by combining the images of multiple smaller display devices. The main objective of this dissertation is the development of new visualization and interaction techniques for large high-resolution displays.